# Thread: Volume as a function of x

1. ## Volume as a function of x

I have a question in my assignment where i am not how to answer it.

A rectangular box with volume 7 cubic metres has a square base with side length x metres. Express the surface area S of the box as a function of x.

Surface area S = ?

I also have these two questions that are along the same lines that i also don't know how to properly solve.

2) The diameter of a spherical balloon is 12 cm. Air is pumped into the balloon to increase its diameter by x cm. Express the increase in volume of air inside the balloon as a function of x.
Note. The volume of a sphere with radius R is V=34 R^3

Answer: The increase in volume is equal to ? cm^3

and

3) A rectangle has its base lying on the x− axis and its upper corners on the parabola y=41−x2. If the upper right corner is (st), express the area A of the rectangle as a function of s.

The area A = ?

2. The volume of a box with a square base will be

$\displaystyle V = x^2h$.

Since the volume is $\displaystyle 7\,\textrm{m}^3$ which means

$\displaystyle x^2h = 7$

$\displaystyle h = \frac{7}{x^2}$.

The surface area is ....

3. Originally Posted by mmfoxall
I have a question in my assignment where i am not how to answer it.

A rectangular box with volume 7 cubic metres has a square base with side length x metres. Express the surface area S of the box as a function of x.

Surface area S = ?

I also have these two questions that are along the same lines that i also don't know how to properly solve.

2) The diameter of a spherical balloon is 12 cm. Air is pumped into the balloon to increase its diameter by x cm. Express the increase in volume of air inside the balloon as a function of x.
Note. The volume of a sphere with radius R is V=34 R^3

Answer: The increase in volume is equal to ? cm^3

and

3) A rectangle has its base lying on the x− axis and its upper corners on the parabola y=41−x2. If the upper right corner is (st), express the area A of the rectangle as a function of s.

The area A = ?